[Retros] die Schwalbe 13237 - Gerald Irsigler

[andrew buchanan]

Hi Mario,

The problem with your 8 attacking queens position is that there are a couple
of pairs which are separated by a knight's move.

It isn't an issue that some of the pieces are on 1st or 8th rank. I agree
with Roberto that we make the sensible assumptions:
(a) exactly 1 king of each colour
(b) no pawns on 1st or 8th ranks

Suppose that it were possible to place 7 non-attacking knight-queens on a
board. Each of them defines an exclusion zone of 5x5 25 squares which no
other knight-queen can enter.

There must be one of these in the central 4x4 square of the board, since
otherwise only 6 can be placed. By symmetry, there are only 3 cases to
consider, and it's just a couple of minutes to check that none of them work
out. Dividing up the remaining area into cells which can accommodate at most
1 knight-queen allows one to prune very quickly.

So 6 is the best for non-attackers + 1 for the extra connected dude gives us
7 as the answer.

Cheers,
Andrew.

-----Original Message-----
From: retros-bounces at janko.at [mailto:retros-bounces at janko.at] On Behalf Of
Mario Richter
Sent: 30 January 2007 17:14
To: andrew at anselan.com; The Retrograde Analysis Mailing List
Subject: Re: [Retros] die Schwalbe 13237 - Gerald Irsigler

Andrew wrote:


> So either of these would work as a 7th point. Can anyone do better? I

don't

> think it's possible.


How about the following position, which is known from the 8 non-attacking
queens problem:

5Q2/2Q5/Q7/7Q/3Q4/1Q6/6Q1/4Q3


regards,

   mario

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